Difference between revisions of "Mock AIME 1 2010 Problems/Problem 1"
Kevin Zhang (talk | contribs) (Created page with 'Since <math>n^2 = 7k+4</math>, <math>n^2</math> is congruent to <math>4</math> mod <math>7</math>. Taking the square root of both sides, we obtain <math>n</math> is congruent to…') |
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Latest revision as of 19:42, 12 March 2010
Since ,
is congruent to
mod
. Taking the square root of both sides, we obtain
is congruent to
mod
. Solving,
is congruent to either
or
mod
. The maximum of
is
, of which the square root is between
and
. So,
must be less than
. The series of solutions for
is
and
. However,
does not work because
, a value not possible for
. Thus, there are
different solutions for a total of
solutions.